What is the function of this normalize?
Normalize (from the blender manual)


  Normalizing a vector scales its magnitude, or length, to a value of 1, but keeps its direction intact.


Why do this for the Z-Pass?

The Z pass is the distance from the camera to the geometry in the scene for every pixel of the image. The camera is the 0 on the scale and the units used for its values are the working units set for the scene (blender units, meters, cm, inches, etc). The Z pass usually has values that exceed the 0 to 1 scale, and thus cannot be displayed as an image.

In order to visualize the information on the Z pass you normalize it so that if fits within the bounds of what can be displayed as an image (o to 1).